| （英） |
Quantum private information retrieval (QPIR) is the problem to retrieve one of f classical files by downloading quantum systems from non-communicating n servers each of which contains the copy of f files, while the identity of the retrieved file is unknown to each server. As an extension, we consider the (n − 1)-private QPIR that the identity of the retrieved file is secret even if any n − 1 servers collude, and derive the QPIR capacity for this problem which is defined as the maximum rate of the retrieved file size over the download size. For an even number n of servers, we show that the capacity of the (n − 1)-private QPIR is 2/n, when we assume that there are preexisting entanglements among the servers and require that no information of the non-retrieved files is downloaded. We construct an (n − 1)-private QPIR protocol of rate ⌈n/2⌉−1 and prove that the capacity is upper bounded by 2/n. The (n − 1)-private QPIR capacity is strictly greater than the classical counterpart. |